(-1)"+1 (3x)" What are all of the values of x ,such that converges? n=1 x>0.1 O 3.3 O .4 O 13 13

Q: What are all of the values of x such that (-1)"*" (3x)" converges? 10 x>0.20 3. r>3.40 1/3

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Q: {B"}-o; ß E (-1,0) A-Converges B-Diverges C-Absolutely converges D-Conditionally converges

A: According to our answering guidelines we can answer one question at a time, therefore I have…

Q: Q2. Find the radius of convergence and interval of convergence of Σ i n! n=0 2"

A: Let us consider the power series ∑n=0∞an(x-a)n There is a positive number R such that , the series…

Q: 2n2 +n+2 ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

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Q: What are all of the values of x ,such that converges? n=1 1>0,1 0 13 X<1 4

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Q: (-1)"3nx" n² – 5 V. Determine the interval of convergence of > n=1

A: This is a problem of series calculation. By using concepts of series we will determine interval of…

Q: E(- 1)n+ 1(n+1," converges conditionally n = 1 Select one: O True O False

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Q: Jlgu (-1)" +1 Σ (3x)" What are all of the values of x ,such that 00 converges? n=1 x>02 C) x>3.3 O

A: Using ratio test the condition of convergence is:…

Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: (x-2) What is the convergency interval of O aR O b. [1,3] O (1,3) O d. (-1,5) O e (-1,5]

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Q: 3 Jlgull What are all of the values of x ,such that (-1)" + '(2n)* converges? 00 n=1 x0.3 0

A: Using ratio test condition of convergence:…

Q: 5. Find all values of x >0 so that ) converges. 3k k=2

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Q: {( 2n The sequence 1+ 2n n=1 Diverges 1 Converges to 1 Converges to Converges to Vē None

A: Ans is given below

Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: 00 1. Find the interval of convergence of 2 n(n + 1)(x – 2)" n=0

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Q: 1 n=1 O a. converges O b. converges to -3 O c. converges to -1 O d. converges to 2 D e. converges to…

A: Explanation of the solution is given below...

Q: (n+1)(2x+1)" 2H (2n+1) a) Find the radius and interval of convergence of

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Q: (x+2)" Find the interval of convergence for 2 n²(-3)" n=1

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Q: What are all of the values of x ,such that (-1)*+(n) * converges? (). x1.40

A: Using ratio test a series converges iff:…

Q: Petermine whether (-1)k converges absolutely, converges conditionally, kl/2 k=1 diverges. or

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Q: What are all of the values of x ,such that converges? n=1 x>0.10 x1.30 x<1.40

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Q: Σ (-1)*2* Use the Ratio Test to determine whether converges absolutely diverges. or k! k=1

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Q: ∞ Find the interval of convergence for n=1 The interval of convergence is a E (x − 4)" n² 3n

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Q: ne wheti wheth the ser 00 (-14)" n! n=0 psolutely convergent onditionally converge

A: Here we have;  ∑n=0∞(-14)nn! ∑n=0∞(-14)nn!=∑n=0∞an   (let)⇒ an=(-14)nn!

Q: (r – 3)* 4. Find all values of x > 0 so that converges. 4k k=2

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Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: (-1)* (k + 1) a* Σ 4k Find the interval of convergence for a) O(-0, 0) b) О (-4,4) с) О (-5, —3) d)…

A: Given : let

Q: +00 2n determine the interval of convergence of (-1)"+1 n3 + 2 n=1

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Q: (x + 2)" Find the interval of convergence for 22(-3)n n²(-3)" n=1

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Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: n 5. Consider the sequence of functions {fn (x)}n given by fn(x) for XE [0,1] and 0 otherwise. Show…

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Q: (-1)*k²(x + 1)* (k + 2)! Find the interval of convergence for a) O[-1,1] 5) O (-0, 00) =) O {1} H) O…

A: given sries ∑-1kk2x+1kk+2!

Q: B. Find the radius and interval check the convergence at the 1. Σ n°(x – 2)n 3n n=1

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Q: (-1)" Σ Find the interval and radius of convergence for: k" n=0

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Q: (-1)" Σ uzt Find the interval and radius of convergence for: k" n=0

A: Here, I have used D'Alembert principle to determine the radius of convergence.

Q: (-1)"x" (a) Find the interval, radius and center of convergence of 3" (n² + 3) n=0

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Q: 6. SELECT ALL APPLICABLE C A) converges by root test 1 10n+1+(-1y" B) converges by ratio test B D. E…

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Q: 2n2 +n+2 Σ ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

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Q: What are all of the values of x ,such that (-1)" -". 00 converges? n=1 x120 x0.4 0

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Q: k Σ (k² + 2)3/2 Use the integral test to determine if converges. k=1 8.

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Q: Inx? x² –1, 2 x=2 A-Converges B-Diverges C- Absolutely converges D-Conditionally converges 8.

A: In both cases we use comparison test.

Q: Q2. Find the radius of convergence and interval of convergence of 5 n! Σ n=0 2"

A: For power series ∑anxn  Radius of convergence is calculated as: 1R=limn→∞¯an+1an Given power series…

Q: Find the interval of convergence for The interval of convergence is a E n=1 (x − 2)" - n² 2n

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Q: (x-n)k Ek=1 27.) Find interval of convergence: 100

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Q: The sequence a=n-vn+1Vn+3 converges to the limit A) -3 B) -1 C) 1 D) +2 E) -2 F) 0

A: For a series ; if it converges then . If  the limit ; then the series diverges.

Q: 5. Consider the sequence of functions {f(x)}n given by f(x) Show that this sequence of functions is…

A: Given sequence of function is {fn(x)}n given by fn(x) =x/n for x∈[0,1] and 0 otherwise.

Q: k2 Use the integral test to determine whether 2 1319)2 converges. (k3 + 9)2 k=1

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Q: Vn2 + 1 Prove that the sequence {an}n=1 converges by following the following sequence of steps. n…

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Q: 3) (z-5)" n-9" 00 Find the interval of convergence of n=D1

A: We have to find the interval of convergence

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.